Harnack Estimate for the Endangered Species Equation

Xiaodong Cao, Mark Cerenzia, Demetre Kazaras

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We prove a differential Harnack inequality for the Endangered Species Equation, which is a nonlinear parabolic equation. Our derivation relies on an idea related to the parabolic maximum principle. As an application of this inequality, we will show that positive solutions to this equation must blow up in finite time.

Original languageEnglish (US)
Pages (from-to)4537-4545
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number10
StatePublished - Oct 1 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


  • Differential Harnack inequality
  • Endangered Species Equation


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